# Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices

11 Aug 2020  ·  Beuzart-Plessis Raphaël ·

This paper contains two results concerning the spectral decomposition, in a broad sense, of the space of nondegenerate Hermitian matrices over a local field of characteristic zero. The first is an explicit Plancherel decomposition of the associated $L^2$ space thus confirming a conjecture of Sakellaridis-Venkatesh in this particular case... The second is a formula for the multiplicities of generic representations in the $p$-adic case that extends previous work of Feigon-Lapid-Offen. Both results are stated in terms of Arthur-Clozel's quadratic local base-change and the proofs are based on local analogs of two relative trace formulas previously studied by Jacquet and Ye and known as (relative) Kuznetsov trace formulas. read more

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Number Theory Representation Theory